How to make an expanding wave ?
If you are not interested in a perfect simulation (with wave interference, variations of the speed, true collisions...), but just a quick animation, I would give a try to the Wave modifier



Suzanne's bust is the origin of the wave. It is animated to go up an down on the Z axis. Then the modifier's wave speed and offste was tweaked to match suzanne's frequency to give the illusion that the two effects are related.

Result: